Principled Probabilistic Imaging using Diffusion Models as Plug-and-Play Priors

TL;DR

This paper introduces a principled Bayesian approach using diffusion models as plug-and-play priors for inverse imaging problems, achieving more accurate reconstructions without approximations.

Contribution

It develops a MCMC-based method that rigorously samples from the posterior using diffusion models, improving upon existing approximation-based approaches.

Findings

More accurate image reconstructions across six inverse problems

Effective posterior estimation demonstrated in real-world black hole imaging

Outperforms existing diffusion model-based inverse methods

Abstract

Diffusion models (DMs) have recently shown outstanding capabilities in modeling complex image distributions, making them expressive image priors for solving Bayesian inverse problems. However, most existing DM-based methods rely on approximations in the generative process to be generic to different inverse problems, leading to inaccurate sample distributions that deviate from the target posterior defined within the Bayesian framework. To harness the generative power of DMs while avoiding such approximations, we propose a Markov chain Monte Carlo algorithm that performs posterior sampling for general inverse problems by reducing it to sampling the posterior of a Gaussian denoising problem. Crucially, we leverage a general DM formulation as a unified interface that allows for rigorously solving the denoising problem with a range of state-of-the-art DMs. We demonstrate the effectiveness of the proposed method on six inverse problems (three linear and three nonlinear), including a real-world black hole imaging problem. Experimental results indicate that our proposed method offers more accurate reconstructions and posterior estimation compared to existing DM-based imaging inverse methods.